deg2rad: Sample longitude and latitude on a sphere

Description

Randomly samples longitude and latitude on earth so that equal areas are (approximately) equally likely to be sampled. (Approximation assumes earth as a perfect sphere.)

Usage

deg2rad(x)
  rad2deg(x)
  xyz2latlon(x, y, z)
  latlon2xyz(latitude, longitude)
  rgeo(n = 1, latlim = c(-90, 90), lonlim = c(-180, 180),
    verbose = FALSE)
  rgeo2(n = 1, latlim = c(-90, 90), lonlim = c(-180, 180),
    verbose = FALSE)
  googleMap(latitude, longitude, position = NULL,
    zoom = 12,
    maptype = c("roadmap", "satellite", "terrain", "hybrid"),
    mark = FALSE, radius = 0, browse = TRUE, ...)

Arguments

a numeric vector

y,z

numeric vectors

latitude,longitude

vectors of latitude and longitude values

number of random locations

latlim,lonlim

range of latitudes and longitudes to sample within, only implemented for rgeo.

verbose

return verbose output that includes Euclidean coordinates on unit sphere as well as longitude and lattitude.

position

a data frame containing latitude and longitude positions

zoom

zoom level for initial map (1-20)

maptype

one of 'roadmap', 'satellite', 'terrain', and 'hybrid'

mark

a logical indicating whether the location should be marked with a pin

radius

a vector of radii of circles centered at position that are displayed on the map

browse

a logical indicating whether the URL should be browsed (else only returned as a string)

...

additional arguments passed to browseURL

Value

a numeric vector
a numeric vector
a matrix each row of which contains a latitude and a longitude value
a matrix each row of which contains the x, y, and z coordinates of a point on a unit sphere
a data frame with variables long and lat. If verbose is TRUE, then x, y, and z coordinates are also included in the data frame.
a data frame with variables long and lat. If verbose is TRUE, then x, y, and z coordinates are also included in the data frame.
a string containing a URL. Optionally, as a side-effect, the URL is visited in a browser

Details

Some additional utility functions are documented here as well.

rgeo and rgeo2 differ in the algorithms used to generate random positions. Each assumes a spherical globe. rgeo uses that fact that each of the x, y and z coordinates is uniformly distributed (but not independent of each other). Furthermore, the angle about the z-axis is uniformly distributed and independent of z. This provides a straightforward way to generate Euclidean coordinates using runif. These are then translated into latitude and longitude.

rgeo2 samples points in a cube by independently sampling each coordinate. It then discards any point outside the sphere contained in the cube and projects the non-discarded points to the sphere. This method must oversample to allow for the discarded points.

Examples

Run this code

deg2rad(180)
rad2deg(2*pi)
xyz2latlon(1,1,1)     # point may be on sphere of any radius
xyz2latlon(0,0,0)     # this produces a NaN for latitude
latlon2xyz(45,45)
rgeo(4)
# sample from a region that contains the continental US
rgeo( 4, latlim=c(25,50), lonlim=c(-65,-125) )
rgeo2(4)